Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.Match each equation to the line of best fit that it models.

Answer 1

Consider the individual graph.

1)

Given:

We get the points (0,2) and (7,3) that lie on the best fit from the graph.

Required:

We need to find the equation of the line.

Step-by-step explanation:

Recall that the y-intercept is the point where the line crosses the y-axis.

At (0,2), the line crosses the y-axis.

The y-intercept, b= 2.

Consider the line equation.

`y=mx+b`

where m is the slope and b is the y-intercept.

Substitute b =2 in the equation.

`y=mx+2`

Substitute x =7 and y =3 in the equation to find the value of m.

`3=m(7)+2`

Solve for m.

`3-2=7m`
`m=(1)/(7)`

Substitute m=1/7 and b =2 in the line equation.

`y=(1)/(7)x+2`

Answer:

`y=(1)/(7)x+2`

2)

Given:

We get the points (0,2) and (7,6) that lie on the best fit from the graph.

Required:

We need to find the equation of the line.

Step-by-step explanation:

Recall that the y-intercept is the point where the line crosses the y-axis.

At (0,2), the line crosses the y-axis.

The y-intercept, b= 2.

Consider the line equation.

`y=mx+b`

where m is the slope and b is the y-intercept.

Substitute b =2 in the equation.

`y=mx+2`

Substitute x =7 and y =6 in the equation to find the value of m.

`6=m(7)+2`

Solve for m.

`6-2=7m`
`m=(4)/(7)`

Substitute m=4/7and b =2 in the line equation.

`y=(4)/(7)x+2`

Answer:

`y=(4)/(7)x+2`

3)

Given:

We get the points (0,2) and (7,1) that lie on the best fit from the graph.

Required:

We need to find the equation of the line.

Step-by-step explanation:

Recall that the y-intercept is the point where the line crosses the y-axis.

At (0,2), the line crosses the y-axis.

The y-intercept, b= 2.

Consider the line equation.

`y=mx+b`

where m is the slope and b is the y-intercept.

Substitute b =2 in the equation.

`y=mx+2`

Substitute x =7 and y =1 in the equation to find the value of m.

`1=m(7)+2`

Solve for m.

`1-2=7m`
`m=(-1)/(7)`

Substitute m= -1/7and b =2 in the line equation.

`y=(-1)/(7)x+2`

Answer:

`y=(-1)/(7)x+2`

4)

Given:

We get the points (0,2) and (6.7) that lie on the best fit from the graph.

Required:

We need to find the equation of the line.

Step-by-step explanation:

Recall that the y-intercept is the point where the line crosses the y-axis.

At (0,2), the line crosses the y-axis.

The y-intercept, b= 2.

Consider the line equation.

`y=mx+b`

where m is the slope and b is the y-intercept.

Substitute b =2 in the equation.

`y=mx+2`

Substitute x =6 and y =7 in the equation to find the value of m.

`7=m(6)+2`

Solve for m.

`7-2=6m`
`m=(5)/(6)`

Substitute m= 5/6 and b =2 in the line equation.

`y=(5)/(6)x+2`

Answer:

`y=(5)/(6)x+2`

`y=(5)/(6)x+2`